Subgroups — #13323592

Order 1792.

648 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#6505	C₂	1	1	yes	maximal, characteristic
3	#11735892	C₂	1	1	yes	maximal, characteristic
4	#11729375	C₂	1	1	yes	maximal, characteristic, complemented
5	#11728709	C₂	1	2	yes	maximal, complemented
6	#11728706	C₂	1	2	yes	maximal, complemented
7	#11728705	C₂	1	2	yes	maximal, complemented
8	#11728704	C₂	1	2	yes	maximal, complemented
9	#11728179	C₂	1	1	yes	maximal, characteristic
10	#11728174	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×#1136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
13	C₂×#6505	C₄	1	1	yes	characteristic
14	C₄×#1157	C₂²	1	1	yes	characteristic
15	C₇×#446	—	2	1	no	—
16	C₇×#446	—	2	1	no	—
17	C₇×#446	C₂²	1	2	yes	—
18	C₇×#446	C₂²	1	2	yes	—
19	C₂×C₇×C₄⋊C₈	—	2	1	no	—
20	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×#97	—	2	1	no	—
22	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
23	#89997	C₄	1	1	yes	characteristic
24	#89883	—	2	1	no	—
25	#89883	—	2	1	no	—
26	#89802	C₄	1	2	yes	—
27	C₄×#1144	C₂²	1	2	yes	—
28	#89798	C₄	1	2	yes	—
29	C₄×#1143	C₂²	1	2	yes	—
30	#89738	C₄	1	1	yes	characteristic
31	#89736	C₄	1	1	yes	characteristic
32	#89697	C₂²	1	1	yes	characteristic
33	#89697	C₂²	1	1	yes	characteristic
34	C₄×#1136	C₂²	1	1	yes	characteristic
35	#89460	C₂²	1	1	yes	characteristic
36	#89460	C₂²	1	1	yes	characteristic
37	C₄×#1131	—	2	1	no	—
38	#89457	—	2	1	no	—
39	#89451	C₂²	1	1	yes	characteristic
40	#89451	C₂²	1	1	yes	characteristic
41	Q₈⋊(C₇⋊C₈)	C₂²	1	2	yes	—
42	Q₈⋊(C₇⋊C₈)	C₂²	1	2	yes	—
43	#89279	C₂²	1	2	yes	—
44	#89278	C₂²	1	2	yes	—
45	#89275	C₂²	1	2	yes	—
46	#89274	C₂²	1	2	yes	—
47	#89249	C₂²	1	2	yes	—
48	C₈×C₇⋊C₈	C₂²	1	2	yes	—
49	#17892	—	7	1	no	maximal, Sylow
50	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
51	C₂×#1157	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₇×C₈	—	2	1	no	—
53	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
55	C₄×C₇×Q₈	—	2	1	no	—
56	C₄×C₇×Q₈	—	2	1	no	—
57	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
58	C₄×C₇×Q₈	C₂³	1	2	yes	—
59	C₂×C₇×C₄⋊C₄	—	2	1	no	—
60	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₇	—	2	1	no	—
62	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
63	C₂×#1144	C₂×C₄	1	2	yes	—
64	#6505	—	2	4	no	—
65	C₂×#1143	C₂×C₄	1	2	yes	—
66	C₄×C₂²⋊D₇	—	2	1	no	—
67	C₄×C₂²⋊D₇	—	2	1	no	—
68	#6489	C₂×C₄	1	1	yes	characteristic
69	C₂×#1136	C₂×C₄	1	1	yes	characteristic
70	C₂×#1136	C₂×C₄	1	1	yes	characteristic
71	C₂×#1131	—	2	1	no	—
72	C₂×#1131	—	2	1	no	—
73	C₄×D₂₈	C₂×C₄	1	1	yes	characteristic
74	C₄×D₂₈	C₂³	1	1	yes	characteristic
75	#6435	—	2	1	no	—
76	C₄²×D₇	—	2	1	no	—
77	C₄×Dic₁₄	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₁₄	C₂³	1	1	yes	characteristic
79	C₇×C₄⋊C₈	—	2	2	no	—
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×C₄⋊C₈	—	2	1	no	—
82	C₇×C₄⋊C₈	C₂³	1	2	yes	—
83	C₇×#97	—	2	2	no	—
84	C₇×#97	—	2	2	no	—
85	C₄×C₇×C₈	D₄	1	1	yes	characteristic
86	C₄×C₇×C₈	D₄	1	1	yes	characteristic
87	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
89	#6409	C₂×C₄	1	2	yes	—
90	#6409	C₂×C₄	1	2	yes	—
91	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
92	C₂²⋊(C₇⋊C₈)	—	2	1	no	—
93	(C₂×D₇)⋊C₈	—	2	1	no	—
94	(C₂×D₇)⋊C₈	—	2	1	no	—
95	#6389	—	2	1	no	—
96	#6389	—	2	1	no	—
97	Dic₇⋊C₈	—	2	1	no	—
98	Dic₇⋊C₈	—	2	1	no	—
99	#6384	C₂×C₄	1	2	yes	—
100	#6383	C₂×C₄	1	2	yes	—
101	#6382	C₂×C₄	1	2	yes	—
102	#6381	C₂×C₄	1	2	yes	—
103	C₄⋊(C₇⋊C₈)	—	2	1	no	—
104	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
105	C₄⋊(C₇⋊C₈)	C₂³	1	1	yes	characteristic
106	#6377	C₂×C₄	1	2	yes	—
107	C₄×C₇⋊C₈	—	2	1	no	—
108	C₄×C₇⋊C₈	C₂³	1	2	yes	—
109	C₄×C₇⋊C₈	C₂³	1	2	yes	—
110	#2965	—	7	1	no	—
111	C₂×#446	D₇	1	1	yes	characteristic, complemented
112	C₄×#137	—	7	1	no	—
113	#1593	—	7	2	no	—
114	#1592	—	7	2	no	—
115	#1591	—	7	2	no	—
116	#1590	—	7	2	no	—
117	#1565	—	7	1	no	—
118	#1479	—	7	1	no	—
119	#1477	—	7	1	no	—
120	C₈×M₁₆	—	7	1	no	—
121	C₂×C₇×Q₈	—	2	1	no	—
122	C₂×C₇×Q₈	—	2	2	no	—
123	C₂×C₇×Q₈	—	2	2	no	—
124	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇	—	2	1	no	—
126	C₂²×C₄×C₇	—	2	1	no	—
127	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	#41	1	1	yes	characteristic
130	C₂×C₂²⋊D₇	—	2	1	no	—
131	#1157	—	2	2	no	—
132	#1157	—	2	2	no	—
133	C₂×D₂₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₇	—	2	1	no	—
135	C₂×C₄×D₇	—	2	1	no	—
136	C₂×C₄×D₇	—	2	1	no	—
137	C₂×Dic₁₄	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	—	2	2	no	—
140	C₂×C₇×C₈	—	4	1	no	—
141	C₂×C₇×C₈	—	4	2	no	—
142	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
146	C₇×C₄⋊C₄	—	2	2	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	2	no	—
149	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
150	C₄²×C₇	—	2	2	no	—
151	C₄²×C₇	—	2	2	no	—
152	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₇	#41	1	1	yes	characteristic
155	C₄²×C₇	C₂⁴	1	1	yes	characteristic
156	C₂²⋊Dic₇	—	2	1	no	—
157	#1144	—	2	4	no	—
158	#1143	—	2	4	no	—
159	(C₂×D₇)⋊C₄	—	2	1	no	—
160	(C₂×D₇)⋊C₄	—	2	1	no	—
161	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
162	C₄⋊Dic₇	C₂²×C₄	1	1	yes	characteristic
163	Dic₇⋊C₄	—	2	1	no	—
164	Dic₇⋊C₄	—	2	1	no	—
165	C₄×Dic₇	—	2	1	no	—
166	C₄×Dic₇	—	2	1	no	—
167	C₄×Dic₇	—	2	1	no	—
168	#1136	—	2	2	no	—
169	#1136	M₁₆	1	4	yes	complemented
170	C₂×C₇⋊C₈	—	2	1	no	—
171	C₂×C₇⋊C₈	—	2	1	no	—
172	C₂×C₇⋊C₈	—	2	2	no	—
173	C₂×C₇⋊C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₇⋊C₈	C₂²×C₄	1	2	yes	—
175	#1131	—	4	2	no	—
176	#1131	—	4	2	no	—
177	C₂×#137	—	7	1	no	—
178	C₄×#41	—	7	1	no	—
179	C₂×C₄×Q₈	C₂×D₇	1	1	yes	characteristic
180	#446	—	2	1	no	—
181	#446	—	2	1	no	—
182	#446	—	7	1	no	—
183	#446	—	7	1	no	—
184	#446	C₂×D₇	1	2	yes	—
185	#446	C₂×D₇	1	2	yes	—
186	#441	—	7	2	no	—
187	#440	—	7	2	no	—
188	C₄×Q₁₆	—	7	2	no	—
189	C₄×SD₁₆	—	7	2	no	—
190	#436	—	7	1	no	—
191	#436	—	7	1	no	—
192	#435	—	14	1	no	—
193	#435	—	14	1	no	—
194	#431	—	7	1	no	—
195	#431	—	7	1	no	—
196	#431	—	14	1	no	—
197	#428	—	7	1	no	—
198	C₂×C₄⋊C₈	—	2	1	no	—
199	C₂×C₄⋊C₈	C₂×D₇	1	1	yes	characteristic
200	#419	—	7	1	no	—
201	#417	—	7	1	no	—
202	C₄×M₁₆	—	7	1	no	—
203	C₄×M₁₆	—	14	1	no	—
204	C₂×#97	—	2	1	no	—
205	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
206	#335	—	7	2	no	—
207	#334	—	7	2	no	—
208	Q₈⋊C₈	—	7	2	no	—
209	Q₈⋊C₈	—	7	2	no	—
210	Q₈⋊C₈	—	7	2	no	—
211	D₄⋊C₈	—	7	2	no	—
212	#322	—	7	2	no	—
213	C₈²	—	7	2	no	—
214	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
215	C₂²×D₇	—	2	1	no	—
216	C₇×Q₈	—	2	2	no	—
217	C₇×Q₈	—	2	2	no	—
218	C₇×Q₈	—	4	2	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	4	1	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	4	2	no	—
226	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
230	C₂×C₄×C₇	#131	1	2	yes	—
231	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
234	C₂²⋊D₇	—	4	2	no	—
235	C₂×Dic₇	—	2	1	no	—
236	C₂×Dic₇	—	2	1	no	—
237	C₂×Dic₇	—	2	1	no	—
238	D₂₈	—	2	1	no	—
239	D₂₈	—	2	1	no	—
240	C₄×D₇	—	4	2	no	—
241	C₄×D₇	—	4	1	no	—
242	C₄×D₇	—	4	1	no	—
243	C₄×D₇	—	4	2	no	—
244	Dic₁₄	—	2	1	no	—
245	Dic₁₄	—	2	1	no	—
246	C₇×C₈	—	2	1	no	—
247	C₇×C₈	—	2	1	no	—
248	C₇×C₈	—	2	1	no	—
249	C₇×C₈	—	4	2	no	—
250	C₇×C₈	#137	1	2	yes	complemented
251	C₇⋊C₈	—	2	2	no	—
252	C₇⋊C₈	—	4	2	no	—
253	C₇⋊C₈	—	4	1	no	—
254	C₇⋊C₈	—	4	1	no	—
255	C₇⋊C₈	C₂×M₁₆	1	4	yes	—
256	C₂×#41	—	7	1	no	—
257	C₂²×Q₈	C₄×D₇	1	1	yes	characteristic
258	#137	—	14	4	no	—
259	C₂×Q₁₆	—	7	2	no	—
260	C₂×SD₁₆	—	7	2	no	—
261	C₂×M₁₆	—	7	1	no	—
262	C₂×M₁₆	—	7	1	no	—
263	C₂×M₁₆	—	14	1	no	—
264	C₂×M₁₆	—	14	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	C₂²⋊D₇	1	1	yes	characteristic
267	C₂²×C₈	C₂²⋊D₇	1	1	yes	characteristic
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	—	7	1	no	—
271	C₄×Q₈	—	7	1	no	—
272	C₄×Q₈	C₄×D₇	1	2	yes	—
273	C₄×Q₈	C₂²×D₇	1	2	yes	—
274	C₄×D₄	—	7	1	no	—
275	C₄×D₄	—	7	1	no	—
276	C₄×D₄	—	14	1	no	—
277	C₄×D₄	—	14	1	no	—
278	#117	—	7	1	no	—
279	#117	—	14	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	C₄×D₇	1	1	yes	characteristic
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	14	1	no	—
284	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
285	#107	—	7	2	no	—
286	#106	—	7	2	no	—
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	7	1	no	—
291	C₄⋊C₈	—	7	1	no	—
292	C₄⋊C₈	—	14	1	no	—
293	C₄⋊C₈	—	14	1	no	—
294	C₄⋊C₈	—	14	1	no	—
295	C₄⋊C₈	C₂²×D₇	1	2	yes	—
296	#103	—	7	2	no	—
297	#103	—	7	2	no	—
298	#103	—	7	2	no	—
299	#102	—	7	2	no	—
300	C₂²⋊C₈	—	14	1	no	—
301	C₂²⋊C₈	—	14	1	no	—
302	C₂²⋊C₈	—	14	1	no	—
303	C₂²⋊C₈	—	14	1	no	—
304	#97	—	2	2	no	—
305	#97	—	2	2	no	—
306	#97	—	7	2	no	—
307	#97	—	14	1	no	—
308	#97	—	14	1	no	—
309	C₄×C₈	—	7	2	no	—
310	C₄×C₈	—	7	2	no	—
311	C₄×C₈	—	14	1	no	—
312	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
313	C₄×C₈	C₂²⋊D₇	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
316	C₂²×C₇	—	2	1	no	—
317	C₂²×C₇	—	2	1	no	—
318	C₂²×C₇	#436	1	2	yes	—
319	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
320	C₂×D₇	—	4	1	no	—
321	C₂×D₇	—	4	1	no	—
322	C₂×D₇	—	4	1	no	—
323	C₄×C₇	—	2	1	no	—
324	C₄×C₇	—	2	1	no	—
325	C₄×C₇	—	2	1	no	—
326	C₄×C₇	—	4	2	no	—
327	C₄×C₇	—	4	2	no	—
328	C₄×C₇	#436	1	2	yes	—
329	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
330	C₄×C₇	C₂×#131	1	1	yes	characteristic
331	C₄×C₇	C₂×#137	1	1	yes	characteristic
332	C₄×C₇	#575	1	1	yes	characteristic
333	Dic₇	—	4	1	no	—
334	Dic₇	—	4	1	no	—
335	Dic₇	—	4	1	no	—
336	#41	—	14	2	no	—
337	#41	—	14	2	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	7	1	no	—
342	C₂×Q₈	C₂×C₄×D₇	1	2	yes	—
343	C₂×D₄	—	7	1	no	—
344	C₂×D₄	—	14	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	14	1	no	—
348	C₂²×C₄	—	14	1	no	—
349	C₂²×C₄	—	14	1	no	—
350	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
351	C₂²×C₄	#1157	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₇	1	1	yes	characteristic
353	Q₁₆	—	14	4	no	—
354	SD₁₆	—	14	4	no	—
355	M₁₆	—	7	4	no	—
356	M₁₆	—	14	2	no	—
357	M₁₆	—	28	2	no	—
358	M₁₆	—	28	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	7	2	no	—
364	C₂×C₈	—	7	2	no	—
365	C₂×C₈	—	14	2	no	—
366	C₂×C₈	—	14	1	no	—
367	C₂×C₈	—	14	1	no	—
368	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
369	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
370	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
371	C₂×C₈	C₂×C₂²⋊D₇	1	1	yes	characteristic
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	7	1	no	—
376	C₄⋊C₄	—	7	1	no	—
377	C₄⋊C₄	—	14	1	no	—
378	C₄⋊C₄	—	14	1	no	—
379	C₄⋊C₄	C₂×C₄×D₇	1	2	yes	—
380	C₂²⋊C₄	—	14	1	no	—
381	C₂²⋊C₄	—	14	1	no	—
382	C₂²⋊C₄	—	14	1	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	14	1	no	—
386	C₄²	—	14	1	no	—
387	C₄²	—	14	1	no	—
388	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
389	C₄²	#1157	1	1	yes	characteristic
390	C₄²	C₂×C₂²⋊D₇	1	1	yes	characteristic
391	C₄²	C₂³×D₇	1	1	yes	characteristic
392	C₂×C₇	—	2	2	no	—
393	C₂×C₇	C₂×#436	1	1	yes	characteristic
394	C₂×C₇	C₄×#137	1	1	yes	characteristic
395	C₂×C₇	#2955	1	1	yes	characteristic
396	D₇	—	8	1	no	—
397	C₂³	—	14	1	no	—
398	C₂³	C₄×C₂²⋊D₇	1	1	yes	characteristic
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	14	1	no	—
403	Q₈	—	14	1	no	—
404	D₄	—	14	1	no	—
405	D₄	—	14	1	no	—
406	D₄	—	28	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	14	1	no	—
415	C₂×C₄	—	14	1	no	—
416	C₂×C₄	—	14	1	no	—
417	C₂×C₄	—	28	2	no	—
418	C₂×C₄	—	28	2	no	—
419	C₂×C₄	—	28	1	no	—
420	C₂×C₄	—	28	1	no	—
421	C₂×C₄	D₇×M₁₆	1	2	yes	—
422	C₂×C₄	#6470	1	2	yes	—
423	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
424	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
425	C₂×C₄	C₄×C₂²⋊D₇	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
427	C₂×C₄	C₂×#1157	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₂²⋊D₇	1	1	yes	characteristic
429	C₈	—	2	1	no	—
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	4	2	no	—
433	C₈	—	7	4	no	—
434	C₈	—	14	2	no	—
435	C₈	—	28	2	no	—
436	C₈	—	28	1	no	—
437	C₈	—	28	1	no	—
438	C₈	#6505	1	2	yes	complemented
439	C₇	#17892	1	1	yes	characteristic, complemented, Sylow
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	28	1	no	—
443	C₂²	—	28	1	no	—
444	C₂²	—	28	1	no	—
445	C₂²	#89900	1	2	yes	—
446	C₂²	C₂×C₄×C₂²⋊D₇	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	28	1	no	—
453	C₄	—	28	1	no	—
454	C₄	—	28	1	no	—
455	C₄	#89900	1	2	yes	—
456	C₄	C₂×D₇×M₁₆	1	1	yes	characteristic
457	C₄	C₂×#6470	1	1	yes	characteristic
458	C₄	C₂×#6505	1	1	yes	characteristic
459	C₄	#90513	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	56	1	no	—
462	C₂	C₄×#6505	1	1	yes	characteristic
463	C₂	C₂×#89900	1	1	yes	characteristic
464	C₂	#11741237	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₄²	C₂³×D₇
Fitting	C₂×C₇×#446	C₂
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×#1157	C₂×C₄
cosocle	C₄²×C₇	C₂⁴
hypercenter	C₂×#446	D₇
hypocenter	C₇	#17892
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#446

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₇×#446	C₂	semidirect
4. #11729375	C₂	semidirect
5. #11728709	C₂	semidirect
6. #11728706	C₂	semidirect
7. #11728705	C₂	semidirect
8. #11728704	C₂	semidirect
10. #11728174	C₂	semidirect
11. C₈×#1136	C₂	semidirect
111. C₂×#446	D₇	semidirect
169. #1136	M₁₆	semidirect
250. C₇×C₈	#137	semidirect
438. C₈	#6505	semidirect
439. C₇	#17892	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#446	2
C₄×#6505	2
#11735892	2
#11729375	2
#11728709	2
#11728706	2
#11728705	2
#11728704	2
#11728179	2
#11728174	2
C₈×#1136	2
#17892	7